Institute for Behavioral Sciences, ETH Zurich, Universitaetsstrasse 6, CAB G84.2, 8092 Zurich, Switzerland.
Dev Psychol. 2010 Jan;46(1):178-92. doi: 10.1037/a0016701.
Interactions between conceptual and procedural knowledge influence the development of mathematical competencies. However, after decades of research, these interrelations are still under debate, and empirical results are inconclusive. The authors point out a source of these problems. Different kinds of knowledge and competencies only show up intertwined in behavior, making it hard to measure them validly and independently of each other. A multimethod approach was used to investigate the extent of these problems. A total of 289 fifth and sixth graders' conceptual and procedural knowledge about decimal fractions was measured by 4 common hypothetical measures of each kind of knowledge. Study 1 tested whether treatments affected the 2 groups of measures in consistent ways. Study 2 assessed, across 3 measurement points, whether conceptual and procedural knowledge could be modeled as latent factors underlying the measures. The results reveal substantial problems with the validities of the measures, which might have been present but gone undetected in previous studies. A solution to these problems is essential for theoretical and practical progress in the field. The potential of the multimethod approach for this enterprise is discussed.
概念性知识和程序性知识之间的相互作用影响着数学能力的发展。然而，经过几十年的研究，这些相互关系仍存在争议，实证结果也没有定论。作者指出了这些问题的一个来源。不同类型的知识和能力在行为中只是交织在一起，这使得很难有效地、独立地对它们进行测量。本研究采用了多方法的方法来调查这些问题的程度。共有 289 名五年级和六年级学生的十进制分数的概念性和程序性知识通过 4 种常见的每种知识的假设测量方法进行了测量。研究 1 检验了处理是否以一致的方式影响这两组测量方法。研究 2 在 3 个测量点上评估了概念性和程序性知识是否可以作为测量方法背后的潜在因素进行建模。结果显示，测量方法的有效性存在很大问题，这些问题在以前的研究中可能存在但未被发现。解决这些问题对于该领域的理论和实践进展至关重要。本文还讨论了多方法方法在这方面的应用潜力。
